What is the following quotient?
3 sqrt 8/4 sqrt 6
To find the quotient, divide the numerator by the denominator.
First, simplify the numerator:
3 sqrt 8 = 3 * 2 sqrt 2 = 6 sqrt 2
Next, simplify the denominator:
4 sqrt 6
The quotient is then (6 sqrt 2) / (4 sqrt 6).
To simplify the division of square roots, we can multiply the numerator and denominator by the conjugate of the denominator. The conjugate of 4 sqrt 6 is 4 sqrt 6.
Thus, the quotient is:
(6 sqrt 2) * (4 sqrt 6) / (4 sqrt 6) * (4 sqrt 6)
Simplifying further:
= (6 * 4) * (sqrt 2 * sqrt 6) / (4 * 4) * (sqrt 6 * sqrt 6)
= 24 sqrt 12 / 16 * 6
= 24 sqrt 12 / 96
= sqrt 12 / 4
Since 12 is a perfect square (4 * 3), we can simplify further:
= sqrt (4 * 3) / 4
= sqrt 4 * sqrt 3 / 4
= 2 sqrt 3 / 4
Final answer: 2 sqrt 3 / 4